In 1954, Attneave (Psychological Review, 61, 183-193) has demonstrated that a line drawing of a sleeping cat could still be identified when the curvature extrema (i.e., points along the contour where the curvature changes maximally) were connected by straight lines. This demonstration has often been cited as evidence for the role of curvature extrema but it has not been examined thoroughly. Here, we do so by showing a large number of subjects (total N = 216) a large number of stimuli (N = 184). We started from outline versions of everyday objects and manipulated them in different ways, depending on the selection criterion for the points to be connected. In Experiment 1, we started from the mathematical curvature singularities. In one variant (Experiment 1a, N = 58), we allowed only one curvature extremum per lob (i.e., a segment of the shape with uniformly positive or uniformly negative curvature) and compared this to a condition with an equal number of inflection points (i.e., points along the contour where curvature changes from positive to negative): Identification was clearly better with extrema (46% correct) than with inflections (20%). In another variant (Experiment 1b, N = 50), the number of extrema and inflections was equated per picture to the number used in Experiment 2 (100% condition), and the same difference became even stronger (53% vs. 14%). In Experiment 2 (N = 108), we used points along the contour which an independent sample of observers had marked as most salient (see De Winter et al., VSS-2002, submitted) or around the points midway between two popular points, and connected either 75 or 100% of the points reaching a pre-defined threshold. In both cases, the straight-line versions connecting the popular points were clearly easier to identify (55 and 69% correct) than those connecting the midpoints (18 and 34%). Results will be discussed in relation to Attneave's original demonstration and other findings about useful information for object recognition.